The long-term objective of this project is to develop powerful and computationally-efficient statistical methods of identifying genes, environmental risk factors and their interactions underlying complex traits related to human diseases and health. The specific aim of this project is to continue to develop survival analysis and genetics models to incorporate age of onset data, environmental covariates information, gene-gene and gene-environment interactions, and multiple disease loci into haplotype-based genetic association analysis, analysis of single nucleotide polymorphisms (SNPs), and admixture mapping of complex traits in population- based cohort studies. The project also evaluates different study designs in genetic association studies. The proposed methods build on current approaches and hinge on novel integration of methods in survival analysis, high-dimensional data analysis and methods in human genetics. The focus will be on the development of rigorous and comprehensive statistical inference procedures for haplotype analysis, gene- gene and gene-environment interaction analysis and admixture mapping in cohort studies of unrelated individuals collected by different study designs, including case-cohort and nested case-control designs. Likelihood-based inferences, hidden Markov models, and threshold gradient descent methods will be developed for these aims. The project will also investigate the robustness, power and efficiencies of these methods, and compare them with existing methods. In addition, this project will develop practical and feasible computer programs in order to implement the proposed methods, and to evaluate the performance of these methods through simulation and application to real data on breast and ovarian cancer risks among the BRCA1/2 carriers and to data sets in the area of pharmacogenomics. The work proposed here will contribute both statistical methodology to studying complex traits and methods for high-dimensional data analysis, and offer insight into each of the clinical areas represented by the various data sets to evaluate these new methods. All programs developed under this grant and detailed documentation will be made available free-of-charge to interested researchers via the World Wide Web.